An on-chip colloidal magneto-optical gratingM. Prikockis, H. Wijesinghe, A. Chen, J. VanCourt, D. Roderick, and R. Sooryakumar Citation: Applied Physics Letters 108, 161106 (2016); doi: 10.1063/1.4947438 View online: http://dx.doi.org/10.1063/1.4947438 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/108/16?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Plasmon-assisted high reflectivity and strong magneto-optical Kerr effect in permalloy gratings Appl. Phys. Lett. 102, 121907 (2013); 10.1063/1.4798657 Benchtop time-resolved magneto-optical Kerr magnetometer Rev. Sci. Instrum. 79, 123905 (2008); 10.1063/1.3053353 Optical manipulation of paramagnetic particles with on-chip detection using spin valve sensors Appl. Phys. Lett. 92, 014105 (2008); 10.1063/1.2829797 Evidence of native oxides on the capping and substrate of Permalloy gratings by magneto-optical spectroscopyin the zeroth- and first-diffraction orders Appl. Phys. Lett. 86, 231101 (2005); 10.1063/1.1944904 Magneto-optical nanoparticle-doped silica-titania planar waveguides Appl. Phys. Lett. 86, 011107 (2005); 10.1063/1.1844038

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An on-chip colloidal magneto-optical grating

M. Prikockis, H. Wijesinghe, A. Chen, J. VanCourt, D. Roderick, and R. Sooryakumara)

Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

(Received 26 January 2016; accepted 12 April 2016; published online 22 April 2016)

Interacting nano- and micro-particles provide opportunities to create a wide range of useful colloi-

dal and soft matter constructs. In this letter, we examine interacting superparamagnetic polymeric

particles residing on designed permalloy (Ni0.8 Fe0.2) shapes that are subject to weak time-orbiting

magnetic fields. The precessing field and magnetic barriers that ensue along the outer perimeter of

the shapes allow for containment concurrent with independent field-tunable ordering of the dipole-

coupled particles. These remotely activated arrays with inter-particle spacing comparable to the

wavelength of light yield microscopic on-chip surface gratings for beam steering and magnetically

regulated light diffraction applications. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4947438]

Diffraction gratings have played an important role in the

development of photonic crystals,1 meta-materials,2 plas-

monics,3 and have been central to technologies spanning from

spectroscopy4 and laser systems,5 to information communica-

tion.6 Initially produced with ruling machines,7 the need for

precise gratings has led to adaption of holographic,8 electron-6

and focused ion beam-based9 methods, to create these optical

elements. Such top-down methods allow fabrication of large

area structures; however, they require serial processing and

often involve long writing times. Particle self-assembly has

recently shown promise for bottom-up construction of peri-

odic patterns, including linear chains10 and close packed

arrays11 to create dynamic diffraction gratings.12 Similarly,

DNA and other surface anchoring techniques have been uti-

lized to pattern fixed gratings on surfaces.13

In this paper, we describe a microscopic colloidal grating

constructed of superparamagnetic beads that self-assemble

into periodic one- or two-dimensional (2-D) structures with

symmetries and spacing adjusted by a weak time-orbiting

magnetic field and underlying lithographically defined perm-

alloy patterns. The role of the permalloy is to confine the

beads by creating a magnetic potential barrier, as discussed in

Ref. 14. The resulting pre-designed magnetic confinement

potentials enable tuning of the diffraction associated with

regulated expansion and collapse of the ordered beads.14

Simulations confirm the observed diffraction symmetries and

their dependence on the initial bead positions. Rotation of

entire ordered clusters relative to the stationary microchip

offers another degree of freedom yielding promising applica-

tions, such as automated beam steering without the need for

mechanical movement. Furthermore, overlapping pattern geo-

metries provide a convenient framework to investigate grain

boundary formation at these length scales in the presence of

particle interactions and Brownian fluctuations.

Figure 1(a) schematically illustrates the primary feature

underlying the colloidal surface grating: a precessing external

magnetic field (HextðtÞ) in relation to a 50 nm thick permalloy

(Py, Ni0.8Fe0.2) pattern. The field, applied remotely via five

orthogonal electromagnets,14 magnetizes 2.8 lm diameter

superparamagnetic beads (Dynabeads, M-270 COOH catalog

# 14305D) and the permalloy. A custom-built reflection

microscope together with a Bertrand lens15 is used to image

the bead clusters and their diffraction patterns. The dipolar

bead coupling and bead-Py containment forces determine the

response of the dipoles. With the precessing field rotating

faster ð> 5 HzÞ than the time required for a dipole to adjust to

the changing potential energy profile, the beads experience

time-averaged forces. The dipole force, quantified for two ad-

jacent beads in Fig. 1(b), shows that the inter-bead interac-

tions can be tuned from attractive to repulsive by fixing the

in-plane magnetic field component ðH1Þ, and varying the field

FIG. 1. (a) Schematic of externally applied precessing magnetic field. (b)

Average in-plane magnetic dipole force experienced by a microbead with an

adjacent bead in an external field of H1 ¼ 30 Oe as a function of the out-of-

plane precession angle, H. (c) Contour plot of time-averaged magnetic

potential energy for a superparamagnetic bead atop a hexagonal Py thin-film

(side length, L=2) for H1 ¼ 30 Oe; H ¼ 45�. The distance between contours

is 500 kBT. (d) Average in-plane confinement forces directed along the x or

y axis. (e) 3-D magnetic potential energy landscapes for a rectangle (left),

hexagon (middle), and a composite of two overlapping Py hexagons (right).

a)E-mail: sooryakumar.1@osu.edu. URL: http://www.physics.ohio-state.edu/

~soory/

0003-6951/2016/108(16)/161106/4/$30.00 Published by AIP Publishing.108, 161106-1

APPLIED PHYSICS LETTERS 108, 161106 (2016)

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16:14:15

angle H. The weight of the microbeads keeps them close to

the sample surface.

Figures 1(c) and 1(d) illustrate the time-averaged mag-

netic potential energy landscape for a superparamagnetic

bead residing on a hexagonal Py film and the confinement

force along the x and y axes. Potential energy profiles from

rectangular, hexagonal, and overlapping Py shapes are

shown in Figure 1(e).

Exploiting the symmetry of a rectangular trap, Figure 2

(top) shows the transition of a two-dimensional (2-D) cluster

into a quasi 1-D line. Microbeads loaded onto the 100 lm �30 lm Py rectangle and a precessing field ðH1 ¼ 35 Oe;H ¼ 25�Þ, results in two rows of ordered particles(Fig. 2(a)).

Reorienting the field to H1 ¼ 35 Oe; H ¼ 90� collapses the

beads to a single row along the long axis of the rectangle (Fig.

2(b)), with corresponding diffraction (Figs. 2(i) and 2(ii)). The

optimal length to width ðL=WÞ ratio to tune the particle order

from 2-D to 1-D is 0.3. Ratios of L=W ¼ 0:2 or 0.4 yield clus-

ters that lift off of the trap, or collapse into a 2-D close-packed

hexagonal lattice, respectively. To achieve the desired

ordering, the upper bound on the areal coverage is

�150 lm2=particle.

Figure 2 (bottom) shows a cluster and its corresponding

diffraction for 655 nm incident light on the hexagonal grating

for various field precession angles ðHÞ. The central 615�

spread of each rear focal plane view is shown. Diffraction

maxima that are clearly visible indicate well-ordered bead

constructs. The separation between diffraction orders widens

as the inter-bead spacing is reduced with increasing H.

Below the critical angle of 54:7� (Fig. 1(b)), for example, at

H ¼ 42� (Fig. 2(d), (iv)), the weakening inter-bead repulsion

affects their spatial order as evidenced by the lack of clarity

in the diffraction pattern, which is recovered as H tends to-

ward 0� or 90�.To study the effect of the initial bead positions on the

emergent diffraction pattern, numerical MATLAB simula-

tions (based on an adaptation of the gradient descent algo-

rithm) were performed with random initial x-y bead

coordinates. The time dependent bead positions are deter-

mined by numerically solving the Langevin equation in low

Reynolds number16

k� 6pgRdr

dt¼ �rU; (1)

where k � 3 is the near wall factor accounting for the nearby

surface, g the fluid viscosity, R and dr/dt the sphere radius

and velocity, and U the average magnetic potential energy

taking into account dipole interactions and the confinement

forces. The consequences of ignoring Brownian motion in

the simulation are discussed below.

The algorithm seeks the nearest local energy minimum

by descending along the steepest slope. Starting with an

N-bead configuration ~rt 2 R3N at time t, the small iterative

change D~rt that brings the system to a lower-energy configu-

ration ~rtþDt ¼~rt þ D~rt is sought under the constraint that a

bead cannot penetrate another bead or the Py shape. Once

the final equilibrium state is reached, a log-scale power spec-

tral density plot is generated using the bead positions in the

x-y plane.

Simulations were run on 165 randomly generated initial

bead positions. Figure 3 shows symmetries observed in the

simulation and corresponding examples from the experi-

ment. “Mixed” symmetry implies that some elements of

multiple rotational symmetries occur within a given cluster.

The number of different symmetries and their frequency of

occurrence in the simulation (percentages in Fig. 3) are con-

sistent with observations. Note that five-fold symmetry has

not been observed, which is plausible based on its rarity

(�1 %) in the simulation.

The results show that the Py shape has limited effect on

the overall symmetry of the confined cluster. Though beads

near the shape edges are influenced by the strong confine-

ment force, that force is transmitted to the rest of the cluster

via dipolar interactions between beads. Since the dipolar

forces are not associated with hard wall potentials, this could

explain why the shapes do not always impose their symmetry

upon the confined cluster.

While six-fold rotational symmetry is most prominent

on hexagonal patterns, oblique square-like symmetries are

also observed. Figure 3, row 1 shows simulations yielding

different symmetries with their corresponding diffraction

patterns presented in row 4. Rows 2 and 3 show the experi-

mental sample plane and diffraction patterns, respectively.

Despite the same field parameters ðH1 ¼ 30 Oe; H ¼ 26�Þ,

FIG. 2. (top) Ordered beads confined on a rectangular 100 lm � 30 lm Py

thin-film. The applied field is H1 ¼ 35 Oe; H ¼ 25�. (a) The field stop is fixed

upon a subset of the confined beads and (i) resulting rear focal plane reveals a

slightly oblique lattice. (b) Precessing field is changed to lie in-plane

(H1 ¼ 35 Oe; H ¼ 90�), collapsing beads into a single line (c). (ii) Zeroth

through second order diffraction maxima are visible. (bottom) Sample (c)–(e)

and rear focal (iii)–(v) planes for 2.8lm beads on hexagonal trap. A central

view of the beads is shown. The white light visible near each zeroth order

maxima is due to a low level of white light used to improve image quality.

161106-2 Prikockis et al. Appl. Phys. Lett. 108, 161106 (2016)

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16:14:15

the clusters sometimes exhibit different symmetries. The dif-

ferences in energy between these configurations are

�4 kBT=bead with the hexagonal configuration being ener-

getically more favorable.

The simulation indicates that the beads are not always

able to move into a hexagonal symmetry because (�26% of

the time, Fig. 3) they can become trapped in another configu-

ration that is a local energy minimum. While thermal energy

may assist the beads in better sampling the configuration

space, barrier energies between hexagonal and other symme-

tries are �7 kBT=bead, indicating that the cluster may not

always find the absolute minimum energy configuration even

with Brownian fluctuations. This statement is supported by

the experimental results and justifies the omission of

Brownian motion in the simulations.

Though multiple symmetries are achievable, only the

most regular and well-ordered bead lattices generally pro-

vide diffraction beyond first order. Higher orders are easily

visible when beads are close-packed because particle contact

stabilizes ordered lattices. However, repulsive dipolar forces,

Brownian fluctuations, differences in particle susceptibility,

and particle-substrate adhesion can often limit spatial order

within the planar lattice resulting in only first (and zeroth)

order diffraction maxima being visible. Nonetheless, this

study offers insight into bead structure symmetry, which has

not typically been the focus of other studies on colloidal

gratings.12,17–19

Another useful feature of the colloidal grating is the

control over the angular orientation of the entire confined

cluster. Figures 4(a) and 4(b) show a cluster which has been

rotated through an in-plane angle, D/ � 40�. The direction

of rotation is easily reversed by switching the field rotation

direction. Figure 4(c) shows the dependence of the cluster

rotation frequency, fc, as a function of the field driving fre-

quency, fd, for ðH1 ¼ 30 Oe; H ¼ 90�Þ. At low fd ð< 5 HzÞ,the beads can respond to the external field, resulting in

breakup and reformation20 of the structure leading to rela-

tively slow rotation times and a low fc. As fd increases, dipo-

lar interactions keep the structure intact, and the cluster

rotation follows linearly with the driving frequency.21 Note

that as a result of fluid drag, fd is about two orders of magni-

tude higher than fc. As shown in Figure 4d, fc also depends

on the cluster size20 with the viscous drag for the entire clus-

ter increasing with the number of particles.

Grain boundaries in solids are lattice defects that affect

scattering processes and influence electrical22 and thermal23

conductivities in 2-D thin-films, or pass bands within pho-

tonic crystal/meta-material devices.24 Thus, understanding

grain boundary formation and their dynamics is essential for

engineering robust materials.25,26 The freedom to create spe-

cific confinement potentials enables the design of polycrys-

talline clusters and grain boundaries by exploiting tunable

interactions and allowing convenient visualization with opti-

cal microscopy.27–29

As an illustration of forming grain boundaries, two

underlying hexagons offset by an angle a ¼ 26� are com-

bined into a single overall polygon (Fig. 4(e)), forcing seg-

ments of the cluster to align with the edges of both

hexagons. The result is a jammed, multi-grain state when the

particles coalesce. The corresponding diffraction pattern

(Fig. 4(f)) reveals an orientation mismatch of 19� between

the two grains. While the deviation from 26� to 19� can be

FIG. 4. (a) and (b) A close packed cluster is rotated, leading to rotation of

the diffraction pattern. (c) The cluster rotation frequency fc as a function of

external field driving frequency, fd. (d) The dependence of fc on the number

of beads in a cluster for fd¼ 20 Hz. The red lines in (c) and (d) are guides to

the eye. (e) A grain boundary formed on a composite Py structure and (f)

corresponding diffraction pattern indicates presence of two distinct grains.

FIG. 3. (row 1) Simulated and (row 2) experimental final bead configura-

tions for various symmetries. (row 3) Corresponding diffraction patterns for

bead configurations of row 2. (row 4) Diffractions patterns calculated from

row 1. The applied field is H1 ¼ 30 Oe; H ¼ 26�. The percentage of simu-

lated final configurations of each symmetry is shown.

161106-3 Prikockis et al. Appl. Phys. Lett. 108, 161106 (2016)

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16:14:15

attributed to the lack of sharpness of the trap potentials, it is

not surprising. When beads are loaded to the edge of the pol-

ygons, they feel the strongest asymmetry in the confinement

force (Fig. 1(d)), which becomes more symmetric toward the

center of the polygon and may allow grain orientations to

shift as the grains coalesce in the middle of the polygon; a

behavior consistent with the force profiles in Figure 1(d) for

jx=Lj; jy=Lj� 0:3. This feature thus offers the opportunity to

directly study the real-time dynamics of grain boundary

formation.

The current micro-grating technology is suited for appli-

cations such as a detector, a specialized optical setup not

requiring fast (<0.5 s) switching times,20 or a monochroma-

tor with no mechanical moving parts. Pairing this grating

with microfluidics, one could build an automated fluid-flow

regulator, using the diffraction to detect (and external fields

to influence) small flow rates in low Reynolds number devi-

ces. Additionally, utilizing particle sizes/spacing on the order

of 1 lm or less could allow for color change applications.

These approaches require faster switches and closer wave-

length matching to the visible such as in magnetic printing,30

security coding of documents,30 optical sensors,31–33 an all-

magnetic color display, or a magneto-optical lock system.

The authors acknowledge useful discussions with

Yuhang Yang. This work was supported in part by the U.S.

Army Research Office under Contract Nos. W911NF-10-1-

0353 and W911NF-14-1-0289.

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